Chapter 3 · Pair of Linear Equations in Two Variables

NCERT Exemplar Class 10 Maths Exercise 3.1

All 13 questions of NCERT Exemplar Class 10 Maths Exercise 3.1 (Pair of Linear Equations in Two Variables), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   Graphically, ​the pair of equations $6x-3y+10=0$ ​and $2x-y+9=0$ represents ​two lines ​which are

   1. (a)intersecting at exactly one point.
   2. (b)intersecting at exactly two points.
   3. (c)coincident.
   4. (d)parallel.
   Show answer

   (d) parallel.

   Step-by-step solution →
2. Q2
   The pair ​of ​equations $x+2y+5=0$ and $-3x-6y+1=0$ ​have

   1. (a)a unique solution
   2. (b)exactly two solutions
   3. (c)infinitely many solutions
   4. (d)no solution
   Show answer

   (d) no solution

   Step-by-step solution →
3. Q3
   If a pair of linear ​equations is ​consistent, ​then ​the ​lines ​will be

   1. (a)parallel
   2. (b)always coincident
   3. (c)intersecting or coincident
   4. (d)always intersecting
   Show answer

   (c) intersecting or coincident

   Step-by-step solution →
4. Q4
   The pair of ​equations $y=0$ ​and $y=-7$ ​has

   1. (a)one solution
   2. (b)two solutions
   3. (c)infinitely many solutions
   4. (d)no solution
   Show answer

   (d) no solution

   Step-by-step solution →
5. Q5
   The pair of ​equations $x=a$ ​and $y=b$ ​graphically represents ​lines ​which are

   1. (a)parallel
   2. (b)intersecting at $(b,a)$
   3. (c)coincident
   4. (d)intersecting at $(a,b)$
   Show answer

   (d) intersecting at $(a,b)$

   Step-by-step solution →
6. Q6
   For ​what ​value ​of $k$, do ​the ​equations $3x-y+8=0$ ​and $6x-ky=-16$ ​represent coincident lines?

   1. (a)$\frac{1}{2}$
   2. (b)$-\frac{1}{2}$
   3. (c)2
   4. (d)$-2$
   Show answer

   (c) 2

   Step-by-step solution →
7. Q7
   If ​the lines given by $3x+2ky=2$ ​and $2x+5y+1=0$ are ​parallel, ​then the value ​of $k$ is

   1. (a)$\frac{-5}{4}$
   2. (b)$\frac{2}{5}$
   3. (c)$\frac{15}{4}$
   4. (d)$\frac{3}{2}$
   Show answer

   (c) $\frac{15}{4}$

   Step-by-step solution →
8. Q8
   The value ​of $c$ for ​which the pair ​of ​equations $cx-y=2$ and $6x-2y=3$ will have ​infinitely many ​solutions is

   1. (a)$3$
   2. (b)$-3$
   3. (c)$-12$
   4. (d)no value
   Show answer

   (d) no value

   Step-by-step solution →
9. Q9
   One equation ​of a pair ​of dependent linear ​equations ​is $-5x+7y=2$. ​The ​second ​equation can ​be

   1. (a)$10x+14y+4=0$
   2. (b)$-10x-14y+4=0$
   3. (c)$-10x+14y+4=0$
   4. (d)$10x-14y=-4$
   Show answer

   (d) $10x-14y=-4$

   Step-by-step solution →
10. Q10
    A pair ​of linear ​equations ​which ​has a ​unique solution $x=2$, $y=-3$ ​is

    1. (a)$x+y=-1$ and $2x-3y=-5$
    2. (b)$2x+5y=-11$ and $4x+10y=-22$
    3. (c)$2x-y=1$ and $3x+2y=0$
    4. (d)$x-4y-14=0$ and $5x-y-13=0$
    Show answer

    (d) $x-4y-14=0$ and $5x-y-13=0$

    Step-by-step solution →
11. Q11
    If $x=a$, $y=b$ is ​the solution ​of ​the equations $x-y=2$ and $x+y=4$, then ​the ​values of $a$ ​and $b$ ​are, respectively

    1. (a)3 and 5
    2. (b)5 and 3
    3. (c)3 and 1
    4. (d)$-1$ and $-3$
    Show answer

    (c) 3 and 1

    Step-by-step solution →
12. Q12
    Aruna has ​only Re 1 ​and Rs 2 coins with ​her. If the total number of coins that she has is 50 and the amount of money with her ​is Rs 75, then ​the number of Re 1 and ​Rs ​2 coins ​are, respectively

    1. (a)35 and 15
    2. (b)35 and 20
    3. (c)15 and 35
    4. (d)25 and 25
    Show answer

    (d) 25 and 25

    Step-by-step solution →
13. Q13
    The father's age is six times his son's age. ​Four ​years ​hence, the age of the father ​will be ​four times his son's age. The ​present ages, ​in years, of the son and the father are, respectively

    1. (a)4 and 24
    2. (b)5 and 30
    3. (c)6 and 36
    4. (d)3 and 24
    Show answer

    (c) 6 and 36

    Step-by-step solution →